Browsing by Subject "Computational electromagnetics"

Now showing 1 - 20 of 27

Open Access
Accelerating the multilevel fast multipole algorithm with the sparse-approximate-inverse (SAI) preconditioning
(Society for Industrial and Applied Mathematics, 2009) Malas, T.; Gürel, Levent
With the help of the multilevel fast multipole algorithm, integral-equation methods can be used to solve real-life electromagnetics problems both accurately and efficiently. Increasing problem dimensions, on the other hand, necessitate effective parallel preconditioners with low setup costs. In this paper, we consider sparse approximate inverses generated from the sparse near-field part of the dense coefficient matrix. In particular, we analyze pattern selection strategies that can make efficient use of the block structure of the near-field matrix, and we propose a load-balancing method to obtain high scalability during the setup. We also present some implementation details, which reduce the computational cost of the setup phase. In conclusion, for the open-surface problems that are modeled by the electric-field integral equation, we have been able to solve ill-conditioned linear systems involving millions of unknowns with moderate computational requirements. For closed surface problems that can be modeled by the combined-field integral equation, we reduce the solution times significantly compared to the commonly used block-diagonal preconditioner.
Open Access
Accuracy and efficiency considerations in the solution of extremely large electromagnetics problems
(IEEE, 2011) Gürel, Levent; Ergül, Özgür
This study considers fast and accurate solutions of extremely large electromagnetics problems. Surface formulations of large-scale objects lead to dense matrix equations involving millions of unknowns. Thanks to recent developments in parallel algorithms and high-performance computers, these problems can easily be solved with unprecedented levels of accuracy and detail. For example, using a parallel implementation of the multilevel fast multipole algorithm (MLFMA), we are able to solve electromagnetics problems discretized with hundreds of millions of unknowns. Unfortunately, as the problem size grows, it becomes difficult to assess the accuracy and efficiency of the solutions, especially when comparing different implementations. This paper presents our efforts to solve extremely large electromagnetics problems with an emphasis on accuracy and efficiency. We present a list of benchmark problems, which can be used to compare different implementations for large-scale problems. © 2011 IEEE.
Open Access
Analysis of double-negative materials with surface integral equations and the multilevel fast multipole algorithm
(IEEE, 2011) Ergül O.; Gürel, Levent
We present a fast and accurate analysis of double-negative materials (DNMs) with surface integral equations and the multilevel fast multipole algorithm (MLFMA). DNMs are commonly used as simplified models of metamaterials at resonance frequencies and are suitable to be formulated with surface integral equations. However, realistic metamaterials and their models are usually very large with respect to wavelength and their accurate solutions require fast algorithms, such as MLFMA. We consider iterative solutions of DNMs with MLFMA and we investigate the accuracy and efficiency of solutions when DNMs are formulated with two recently developed formulations, namely, the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE). Numerical results on canonical objects are consistent with previous results in the literature on ordinary objects. © 2011 IEEE.
Open Access
Approximate MLFMA as an efficient preconditioner
(IEEE, 2007) Malas, Tahir; Ergül, Özgür; Gürel, Levent
In this work, we propose a preconditioner that approximates the dense system operator. For this purpose, we develop an approximate multilevel fast multipole algorithm (AMLFMA), which performs a much faster matrix-vector multiplication with some relative error compared to the original MLFMA. We use AMLFMA to solve a closely related system, which makes up the preconditioner. Then, this solution is embedded in the main solution that uses MLFMA. By taking into account the far-field elements wisely, this preconditioner proves to be much more effective compared to the near-field preconditioners.
Open Access
An effective preconditioner based on schur complement reduction for integral-equation formulations of dielectric problems
(IEEE, 2009) Malas, Tahir; Gürel, Levent
The author consider effective preconditioning of recently proposed two integral-equation formulations for dielectrics; the combined tangential formulation (CTF) and the electric and magnetic current combined-field integral equation (JMCFIE). These two formulations are of utmost interest since CTF yields more accurate results and JMCFIE yields better-conditioned systems than other formulations.
Open Access
Fast and accurate analysis of optical metamaterials using surface integral equations and the parallel multilevel fast multipole algorithm
(IEEE, 2013) Ergül, Özgür; Gürel, Levent
We present fast and accurate simulations of optical metamaterials using surface integral equations and the multilevel fast multipole algorithm (MLFMA). Problems are formulated with the electric and magnetic current combined-field integral equation and solved iteratively with MLFMA, which is parallelized using the hierarchical strategy on distributed-memory architectures. Realistic metamaterials involving dielectric, perfectly conducting, and plasmonic regions of finite extents are solved rigorously with the developed implementation without any periodicity assumptions.
Open Access
Fast and accurate solutions of extremely large integral-equation problems discretised with tens of millions of unknowns
(The Institution of Engineering and Technology, 2007) Gürel, Levent; Ergül, Özgür
The solution of extremely large scattering problems that are formulated by integral equations and discretised with tens of millions of unknowns is reported. Accurate and efficient solutions are performed by employing a parallel implementation of the multilevel fast multipole algorithm. The effectiveness of the implementation is demonstrated on a sphere problem containing more than 33 million unknowns, which is the largest integral-equation problem ever solved to our knowledge.
Open Access
Fast and accurate solutions of large-scale scattering problems with parallel multilevel fast multipole algorithm
(IEEE, 2007) Ergül, Özgür; Gürel, Levent
Fast and accurate solution of large-scale scattering problems obtained by integral-equation formulations for conducting surfaces is considered in this paper. By employing a parallel implementation of the multilevel fast multipole algorithm (MLFMA) on relatively inexpensive platforms. Specifically, the solution of a scattering problem with 33,791,232 unknowns, which is even larger than the 20-million unknown problem reported recently. Indeed, this 33-million-unknown problem is the largest integral-equation problem solved in computational electromagnetics.
Open Access
Fast direct (noniterative) solvers for integral-equation formulations of scattering problems
(IEEE, 1998) Gürel, Levent; Chew, W. C.
A family of direct (noniterative) solvers with reduced computational complexity is proposed for solving problems involving resonant or near-resonant structures. Based on the recursive interaction matrix algorithm, the solvers exploit the aggregation concept of the recursive aggregate T-matrix algorithm to accelerate the solution. Direct algorithms are developed to compute the scattered field and the current coefficient, and invert the impedance matrix. Computational complexities of these algorithms are expressed in terms of the number of harmonics P required to express the scattered field of a larger scatterer made up of N scatterers. The exact P-N relation is determined by the geometry.
Open Access
Hierarchical parallelization of the multilevel fast multipole algorithm (MLFMA)
(IEEE, 2013) Gürel, Levent; Ergül, Özgür
Due to its O(N log N) complexity, the multilevel fast multipole algorithm (MLFMA) is one of the most prized algorithms of computational electromagnetics and certain other disciplines. Various implementations of this algorithm have been used for rigorous solutions of large-scale scattering, radiation, and miscellaneous other electromagnetics problems involving 3-D objects with arbitrary geometries. Parallelization of MLFMA is crucial for solving real-life problems discretized with hundreds of millions of unknowns. This paper presents the hierarchical partitioning strategy, which provides a very efficient parallelization of MLFMA on distributed-memory architectures. We discuss the advantages of the hierarchical strategy over previous approaches and demonstrate the improved efficiency on scattering problems discretized with millions of unknowns. © 1963-2012 IEEE.
Open Access
Improving the accuracy of the surface integral equations for low-contrast dielectric scatterers
(IEEE, 2007) Ergül, Özgür; Gürel, Levent
Solutions of scattering problems involving low-contrast dielectric objects are considered by employing surface integral equations. A stabilization procedure based on extracting the non-radiating part of the induced currents is applied so that the remaining radiating currents can be modelled appropriately and the scattered fields from the low-contrast objects can be calculated with improved accuracy. Stabilization is applied to both tangential (T) and normal (N) formulations in order to use the benefits of different formulations.
Open Access
Iterative near-field preconditioner for the multilevel fast multipole algorithm
(Society for Industrial and Applied Mathematics, 2010-07-06) Gürel, Levent; Malas, T.
For iterative solutions of large and difficult integral-equation problems in computational electromagnetics using the multilevel fast multipole algorithm (MLFMA), preconditioners are usually built from the available sparse near-field matrix. The exact solution of the near-field system for the preconditioning operation is infeasible because the LU factors lose their sparsity during the factorization. To prevent this, incomplete factors or approximate inverses can be generated so that the sparsity is preserved, but at the expense of losing some information stored in the near-field matrix. As an alternative strategy, the entire near-field matrix can be used in an iterative solver for preconditioning purposes. This can be accomplished with low cost and complexity since Krylov subspace solvers merely require matrix-vector multiplications and the near-field matrix is sparse. Therefore, the preconditioning solution can be obtained by another iterative process, nested in the outer solver, provided that the outer Krylov subspace solver is flexible. With this strategy, we propose using the iterative solution of the near-field system as a preconditioner for the original system, which is also solved iteratively. Furthermore, we use a fixed preconditioner obtained from the near-field matrix as a preconditioner to the inner iterative solver. MLFMA solutions of several model problems establish the effectiveness of the proposed nested iterative near-field preconditioner, allowing us to report the efficient solution of electric-field and combined-field integral-equation problems involving difficult geometries and millions of unknowns.
Open Access
Iterative solution of the normal-equations form of the electric-field integral equation
(IEEE, 2007) Ergül, Özgür; Gürel, Levent
In this paper, we show that transforming the original equations into normal equations improves the convergence of EFIE significantly. We present the solutions of EFIE by employing the least-squares QR (LSQR) algorithm, which corresponds to a stable application of the conjugate gradient (CG) algorithm on the normal equations. Despite the squaring of the condition number due to such a transformation into the normal equations, LSQR improves the convergence rate of the iterative solutions of EFIE and performs better than many other iterative algorithms that are commonly used in the literature. In addition to LSQR, we present the accelerated convergence of the normal equations in the context of the generalized minimal residual (GMRES) algorithm, where the memory requirement is reduced significantly due to the improved convergence characteristics.
Open Access
Microwave imaging of three-dimensional conducting objects using the newton minimization approach
(IEEE, 2013) Etminan, A.; Gürel, Levent
In this work, we present a framework to detect the shape of unknown perfect electric conducting objects by using inverse scattering and microwave imaging. The initialguess object, which evolves to achieve the target, is modeled by triangles such that vertices of the triangles are the unknowns of our problem.
Open Access
On the choice of basis functions to model surface electric current densities in computational electromagnetics
(Wiley-Blackwell Publishing, Inc., 1999-11) Gürel, Levent; Sertel, K.; Şendur, İ. K.
Basis functions that are used to model surface electric current densities in the electric field integral equations of computational electromagnetics are analyzed with respect to how well they model the charge distribution, in addition to the current. This analysis is carried out with the help of the topological properties of open and closed surfaces meshed into networks of triangles and quadrangles. The need for current basis functions to properly model the charge distribution is demonstrated by several examples. In some of these examples, the basis functions seem to be perfectly legitimate when only the current distribution is considered, but they fail to deliver a correct solution of the electromagnetic problem, since they are not capable of properly modeling the charge distribution on some surfaces. Although the idea of proper modeling of the charge distribution by the current basis functions is easy to accept and can even be claimed well known, the contrary uses encountered in the literature have been the motivation behind the investigation reported in this paper.
Open Access
On the Lagrange interpolation in multilevel fast multipole algorithm
(IEEE, 2006) Ergül, Özgür; Gürel, Levent
We consider the Lagrange interpolation employed in the multilevel fast multipole algorithm (MLFMA) as part of our efforts to obtain faster and more efficient solutions for large problems of computational electromagnetics. For the translation operator, we present the choice of the parameters for optimal interpolation. For the aggregation and dissaggregation processes, we discuss the interpolation matrices and introduce an efficient way of improving the accuracy by employing the poles.
Open Access
A performance-enhanced planar Schottky diode for Terahertz applications: an electromagnetic modeling approach
(Cambridge University Press, 2017) Ghobadi, Amir; Khan, Talha Masood; Celik, Ozan Onur; Biyikli, Necmi; Okyay, Ali Kemal; Topalli, Kagan
In this paper, we present the electromagnetic modeling of a performance-enhanced planar Schottky diode for applications in terahertz (THz) frequencies. We provide a systematic simulation approach for analyzing our Schottky diode based on finite element method and lumped equivalent circuit parameter extraction. Afterward, we use the developed model to investigate the effect of design parameters of the Schottky diode on parasitic capacitive and resistive elements. Based on this model, device design has been improved by deep-trench formation in the substrate and using a closed-loop junction to reduce the amount of parasitic capacitance and spreading resistance, respectively. The results indicate that cut-off frequency can be improved from 4.1 to 14.1 THz. Finally, a scaled version of the diode is designed, fabricated, and well characterized to verify the validity of this modeling approach.
Open Access
Preconditioning large integral-equation problems involving complex targets
(IEEE, 2008-07) Malas, Tahir; Gürel, Levent
When the target problem is small in terms of the wavelength, simple preconditioners, such as BDP, may sufficiently accelerate the convergence. On the other hand, for large-scale problems, the matrix equations become much more difficult to solve, and therefore, the importance of preconditioning become more evident for both formulations. In this paper, we demonstrate the use of novel, strong, and efficient preconditioners for the solutions of large EFIE and CFIE problems.
Open Access
Reducing MLFMA memory with out-of-core implementation and data-structure parallelization
(IEEE, 2013) Hidayetoğlu, Mert; Karaosmanoğlu, Barışcan; Gürel, Levent
We present two memory-reduction methods for the parallel multilevel fast multipole algorithm (MLFMA). The first method implements out-of-core techniques and the second method parallelizes the pre-processing data structures. Together, these methods decrease parallel MLFMA memory bottlenecks, and hence fast and accurate solutions can be achieved for largescale electromagnetics problems.
Open Access
Rigorous solutions of large-scale dielectric problems with the parallel multilevel fast multipole algorithm
(IEEE, 2011) Ergül, Özgür; Gürel, Levent
We present fast and accurate solutions of large-scale electromagnetics problems involving three-dimensional homogeneous dielectric objects. Problems are formulated rigorously with the electric and magnetic current combined-field integral equation (JMCFIE) and solved iteratively with the multilevel fast multipole algorithm (MLFMA). In order to solve large-scale problems, MLFMA is parallelized efficiently on distributed-memory architectures using the hierarchical partitioning strategy. Efficiency and accuracy of the developed implementation are demonstrated on very large scattering problems discretized with tens of millions of unknowns. © 2011 IEEE.